# Which of the bulbs glow brightest and least bright?

• Jahnavi
In summary: I cannot but concede the point as you are right, and a low thermal resistivity is specified, but I wonder whether this simplification does more harm than good when it comes to understanding the nature of how a filament lamp works.
Jahnavi

## Homework Equations

Power of a bulb = I2R = V2/R

## The Attempt at a Solution

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From the ratings given on the bulbs using P=V2/R , we can conclude that resistances of the bulbs in decreasing order are R , P , Q i.e R has highest resistance and Q has lowest .

Now brightness is related to power dissipated .

Using P= I2R and the fact that both the current flowing in , as well as resistor of R is highest , so power dissipated in R should be highest .

Now potential difference across P and Q is same and resistance of P is more than that of Q , so using V2/R , power dissipated in P should be lower .

Hence least bright should be P . But R,P is not an option .

What is the mistake ?

#### Attachments

• bulbs.jpg
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I think your analysis is correct. It should indeed be R, P.

Current through R is the sum of the currents through P and Q, and its resistance is more than the resistances of P and Q. Hence, it should be the brightest. The dimmer one between P and Q is the dimmest bulb.

Jahnavi
Your first conclusion would be correct if the bulbs all had the same voltage across them, but they don't.

magoo said:
Your first conclusion would be correct if the bulbs all had the same voltage across them, but they don't.

Are you suggesting that R is not the brightest ?

If you work out all the resistances, voltages and powers you get

P=2.4W
Q=4W
R=25.6W

So R, P is correct. The book answer is wrong.

Jahnavi
1. Bulb resistance calculated from rated wattage and voltage yields the hot resistance obtained when the bulbs are operated at rated voltage.
Are any of them operating at rated voltage?
2. What happens to resistance as filament temperature decreases? How does this affect the actual wattage dissipated by each bulb?

cnh1995 said:
I think your analysis is correct. It should indeed be R, P.

Current through R is the sum of the currents through P and Q, and its resistance is more than the resistances of P and Q. Hence, it should be the brightest. The dimmer one between P and Q is the dimmest bulb.

Thanks for confirming .

CWatters said:
If you work out all the resistances, voltages and powers you get

P=2.4W
Q=4W
R=25.6W

So R, P is correct. The book answer is wrong.

Yes . I get the same result .

Thanks .

Asymptotic said:
1. Bulb resistance calculated from rated wattage and voltage yields the hot resistance obtained when the bulbs are operated at rated voltage.
Are any of them operating at rated voltage?
2. What happens to resistance as filament temperature decreases? How does this affect the actual wattage dissipated by each bulb?
It is mentioned in the problem that the bulbs have a low thermal resistivity coefficient.
Doesn't it mean that we can assume the resistances to be temperature independent as the variation of resistance with temperature is small?

CWatters and Jahnavi
cnh1995 said:
It is mentioned in the problem that the bulbs have a low thermal resistivity coefficient.
Doesn't it mean that we can assume the resistances to be temperature independent as the variation of resistance with temperature is small?
Constantan, for example, has a negligible thermal resistivity coefficient, but isn't a practical material for incandescent filament manufacture. I cannot but concede the point as you are right, and a low thermal resistivity is specified, but I wonder whether this simplification does more harm than good when it comes to understanding the nature of how a filament lamp works.

cnh1995

## 1. Why do some bulbs glow brighter than others?

The brightness of a bulb is determined by the amount of electric current flowing through it. The higher the current, the brighter the bulb will glow. Factors such as the type of bulb, voltage, and wattage also play a role in determining the brightness.

## 2. Are all bulbs with the same wattage equally bright?

No, the wattage of a bulb only indicates the amount of power it consumes, not its brightness. Different types of bulbs, such as incandescent, fluorescent, and LED, have different levels of efficiency and therefore may have different levels of brightness with the same wattage.

## 3. What is the difference between lumens and watts in terms of bulb brightness?

Lumens measure the amount of light emitted by a bulb, while watts measure the amount of power consumed by the bulb. In general, the higher the lumens, the brighter the bulb will be. However, the relationship between lumens and watts can vary depending on the type of bulb.

## 4. Can the brightness of a bulb be adjusted?

Yes, the brightness of some bulbs can be adjusted through a dimmer switch. This controls the amount of electric current flowing through the bulb, thus affecting its brightness. However, not all types of bulbs are dimmable.

## 5. How can I determine the brightness of a bulb before purchasing it?

You can look at the lumens rating of the bulb, which is typically listed on the packaging. You can also compare the wattage and type of bulb to get an idea of its brightness. Additionally, you can read reviews or ask for recommendations from others who have used the same bulb.

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